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Block #2,585,734

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/26/2018, 12:01:15 AM · Difficulty 11.2601 · 4,259,403 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

ce01954ff7eed676ee314d000090733a9f83e9b03b8c56bfb8b5def69332cbb5

View on Chainz ↗

Height

#2,585,734

Difficulty

11.260091

Transactions

Size

202 B

Version

Bits

0b429554

Nonce

816,176,993

Timestamp

3/26/2018, 12:01:15 AM

Confirmations

4,259,403

Merkle Root

218d4f64a3d4e363ab2fb9150952f56a750308b8cc6689c8ac8bc2b971433c92

Transactions (1)

Coinbase218d4f64a3d4e3…8bc2b971433c92

1 in → 1 out7.8700 XPM110 B

AXnDS4Hg…k68s3UBk

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

9.764 × 10⁹⁸(99-digit number)

97644035283068775841…34463644220923576320

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

9.764 × 10⁹⁸(99-digit number)

97644035283068775841…34463644220923576319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.764 × 10⁹⁸(99-digit number)

97644035283068775841…34463644220923576321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.952 × 10⁹⁹(100-digit number)

19528807056613755168…68927288441847152639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.952 × 10⁹⁹(100-digit number)

19528807056613755168…68927288441847152641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

3.905 × 10⁹⁹(100-digit number)

39057614113227510336…37854576883694305279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.905 × 10⁹⁹(100-digit number)

39057614113227510336…37854576883694305281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

7.811 × 10⁹⁹(100-digit number)

78115228226455020672…75709153767388610559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.811 × 10⁹⁹(100-digit number)

78115228226455020672…75709153767388610561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.562 × 10¹⁰⁰(101-digit number)

15623045645291004134…51418307534777221119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.562 × 10¹⁰⁰(101-digit number)

15623045645291004134…51418307534777221121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.124 × 10¹⁰⁰(101-digit number)

31246091290582008269…02836615069554442239

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page →

★★★☆☆

Rarity

RareChain length 11

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 2585734

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock ce01954ff7eed676ee314d000090733a9f83e9b03b8c56bfb8b5def69332cbb5

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,585,734 on Chainz ↗

Block #2,585,734

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